Find an equation of the tangent line to the curve at the given point ? y= (sqrt x) , (49,7)

First we can find the slope of your tangent calculating the derivative of your function and substituting the value ##x=49## in it: 1) ##f(x)=sqrt(x)## ##f'(x)=1/(2sqrt(x))## 2) for ##x=49## you get: ##f'(49)=1/(2sqrt(49))=1/14## 3) the equation of the tangent with slope ##m=1/14## and passing through (##x_0=49, y_0=7##) can be written as: ##y-y_0=m(x-x_0)## ##y-7=1/14(x-49)## ##y=x/14+7/2##

Graphically: